Question

If the radius of a circle is 5 centimeters, how long is the arc subtended by an angle measuring 60°? A) 3 5 π cm B) 5 2 π cm C) 5 3 π cm D) 5 6 π cm

Answer 1

The length of the arc is
`(5\pi)/(3)` centimeters.

Explanation:

The length of an arc (
`\Delta s`) with a given central angle is determined by the following expression:

`\Delta s = (\theta)/(360^(\circ))\cdot 2\pi\cdot r`

Where:

`r` - Radius, measured in centimeters.

`\theta` - Central angle, measured in sexagesimal degrees.

Given that
`r = 5\,cm` and
`\theta = 60^(\circ)`, then:

`\Delta s = (60^(\circ))/(360^(\circ)) * 2\pi * 5\,cm`

`\Delta s = (5\pi)/(3)\,cm`

The length of the arc is
`(5\pi)/(3)` centimeters.